Let $f(x) = 3x^{2}+8x+5$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Answer: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $3x^{2}+8x+5 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 3, b = 8, c = 5$ $ x = \dfrac{-8 \pm \sqrt{8^{2} - 4 \cdot 3 \cdot 5}}{2 \cdot 3}$ $ x = \dfrac{-8 \pm \sqrt{4}}{6}$ $ x = \dfrac{-8 \pm 2}{6}$ $x =-1,-\frac{5}{3}$